Electronic transport through a parallel-coupled triple quantum dot molecule: Fano resonances and bound states in the continuum

In this paper we study electronic transport through a triple quantum dot molecule attached in parallel to leads in presence of a magnetic flux. We have obtained analytical expressions of the linear conductance and density of states for the molecule in equilibrium at zero temperature. As a consequence of quantum interference, the conductance exhibits one Breit-Wigner and two Fano resonances, which positions and widths are controlled by the magnetic field. Every two flux quanta, there is an inversion of roles of the bonding and antibonding states. For particular values of the magnetic flux and dot-lead couplings, one or even both Fano resonances collapse and bound states in the continuum (BICs) are formed. We examine the line broadenings of the molecular states as a function of the Aharonov-Bohm phase around the condition for the formation of BICs, finding resonances which keep extremely narrow against variations of the magnetic field. Moreover, we analyze a molecule of $N$ quantum dots in the absence of magnetic field, showing that certain symmetries lead to a determinate quantity of simultaneous BICs.

Figure 1

Triple quantum dot molecule coupled in parallel to leads.

Figure 2

Dimensionless conductance versus Fermi energy, in units of $\gamma$, for $V_1=V_2=V_3=V$, $t=2$, (a) $\varphi =0$ (solid line) and $\varphi =\pi ∕5$ (dash line), (b) $\varphi =3\pi ∕4$, (c) $\varphi =\pi$ (solid line), and $\varphi =6\pi ∕5$ (dash line) (d) $\varphi =2\pi$, for ${\omega }_0=0$.

Figure 3

Density of state versus Fermi energy, in units of $\gamma$, for $V_1=V_2=V_3=V$, $t=2$, (a) $\varphi =0$, (b) $\varphi =3\pi ∕4$, (c) $\varphi =\pi$, and (d) $\varphi =2\pi$, and ${\omega }_0=0$

Figure 4

Broadenings of the molecular states ${\Gamma }_{-}$, ${\Gamma }_0$, and ${\Gamma }_{+}$ as a function of $\varphi$, for $V_1=V_2=V_3=V$ and $t=2$.

Figure 5

Dimensionless conductance versus Fermi energy, in units of $\gamma$, for $V_1=V_3=V$, $V_2=\sqrt{2}V$, $t=2$, (a) $\varphi =0$ (solid line) and $\varphi =\pi ∕5$ (dash line), (b) $\varphi =3\pi ∕4$, (c) $\varphi =\pi$ (solid line), and $\varphi =6\pi ∕5$ (dash line), (d) $\varphi =2\pi$, and ${\omega }_0=0$.

Figure 6

Density of state versus Fermi energy, in units of $\gamma$, for $V_1=V_3=V$, $V_2=\sqrt{2}V$, $t=2$, (a) $\varphi =0$, (b) $\varphi =3\pi ∕4$, (c) $\varphi =\pi$, and (d) $\varphi =2\pi$, for ${\omega }_0=0$.

Figure 7

Broadenings of the molecular states ${\Gamma }_{-}$, ${\Gamma }_0$, and ${\Gamma }_{+}$ as a function of $\varphi$, for $V_1=V_3=V$, $V_2=\sqrt{2}V$, and $t=2$.